Please can you help me with a problem with specifying content for the footer columns?

In the first column I have the text widget with some HTML. It shows up fine.

In the second column I have some PHP to show titles of posts. I know this works since I have used it in a previous theme.

In the third column I have another PHP snippet to show and RSS feed of Flickr images. Also, this worked in a previous theme.

In the fourth column, I have again some HTML. But this time it does not execute.

Plain text with no code shows up fine in each of the columns. So for some reason the code in the 2nd, 3rd and 4th columns is not executing. I used a plugin Exec-PHP to see if that would make the PHP work, but it didn’t. Please can you help me figure out how to execute the code in the footer box widgets?